Question

Repeat part b) of the preceding problem for Minneapolis in January, assuming a lower efficiency of 32% (because of higher energy losses at the lower ambient temperature).   

Table 9.1 data for Minneapolis: (average monethly insolation [W/m^2] and temperature)

January: horizontal- 75 tilted at latitude- 146 average temp(C)- -11.2

June: horizontal- 263 tilted at latitude- 233 average temp(C)- 16.4

September: horizontal- 171 tilted at latitude- 208 average temp(C)- 15.8

Preceding problem states:

A household in Albuquerque uses 100 gallons of hot water per day (1 gallon of water has a mass of 3.78kg), and the water temperature must be raised from 10 degrees C to 50 degrees C.   a) Find the average power needed to heat the water b) Assume the house has solar collectors with 55% average efficiency at converting sunlight to thermal energy which tilted at Albuquerque's latitude. Use data from Table 9.1 to find the collector area to supply this power in June.

Data needed from table 9.1: (average monthly insolation (W/m62) and temperature for selected US cities   

Albuquerque-              January: horizontal- 133    tilted at latitude- 221      Average temp (C)- 1.2

June: horizontal- 338      tilted at latitude- 296       Average temp (C)- 23.4  

September:     horizontal- 246        tilted at latitude- 283       Average temp (C)- 20.3

Answer 1

Firstly, we need to find average energy for the Albuduerque household

Q = mc t

Q = Thermal energy, m = mass of water, c = specific heat of water which is 4186 j/kg ⁰C , t= 50-10 = 40 ⁰C

= (100*3.78)*4186 * 40 = 63292320 J / kg

So, Power = Energy / time ( time = 24hours *60*60 = 86400)

= 63292320 / 86400 = 732 W

(b) Efficiency in Minneapolis is 32 %

So, 32% of x = 732 (where x is total Power)

=> x = 732 *100 / 32 = 2287 W

Now , 1 m² of panel collects 146 W (given for Jan)

The number of square metres required by 2287 W of power to be generated is ,

So, 2287 / 146 = 15.6 m²

( i have assumed the reference to preceding question is given so as to calculate Power, and the inputs of 100 gallons and temperature are same for Minneapolis Question too, If it's otherwise you can calculate using the above method by putiing in the different values)